diff --git a/include/haproxy/connection-t.h b/include/haproxy/connection-t.h
index 6ee0940be..83969da06 100644
--- a/include/haproxy/connection-t.h
+++ b/include/haproxy/connection-t.h
@@ -473,7 +473,7 @@ struct conn_src {
  * CAUTION! Always update CONN_HASH_PARAMS_TYPE_COUNT when adding a new entry.
  */
 enum conn_hash_params_t {
-	CONN_HASH_PARAMS_TYPE_SNI      = 0x1,
+	CONN_HASH_PARAMS_TYPE_NAME     = 0x1,
 	CONN_HASH_PARAMS_TYPE_DST_ADDR = 0x2,
 	CONN_HASH_PARAMS_TYPE_DST_PORT = 0x4,
 	CONN_HASH_PARAMS_TYPE_SRC_ADDR = 0x8,
@@ -494,7 +494,7 @@ enum conn_hash_params_t {
  * connection hash.
  */
 struct conn_hash_params {
-	uint64_t sni_prehash;
+	uint64_t name_prehash;
 	uint64_t proxy_prehash;
 	uint64_t mark_tos_prehash;
 	void *target;
diff --git a/include/haproxy/connection.h b/include/haproxy/connection.h
index 91ddcd6a5..aa61cc71a 100644
--- a/include/haproxy/connection.h
+++ b/include/haproxy/connection.h
@@ -97,7 +97,7 @@ void sockaddr_free(struct sockaddr_storage **sap);
 
 /* connection hash stuff */
 uint64_t conn_calculate_hash(const struct conn_hash_params *params);
-uint64_t conn_hash_prehash(char *buf, size_t size);
+uint64_t conn_hash_prehash(const char *buf, size_t size);
 
 int conn_reverse(struct connection *conn);
 
diff --git a/src/backend.c b/src/backend.c
index e5444988c..d74ae4082 100644
--- a/src/backend.c
+++ b/src/backend.c
@@ -1349,9 +1349,7 @@ int connect_server(struct stream *s)
 	int reuse = 0;
 	int init_mux = 0;
 	int err;
-#ifdef USE_OPENSSL
-	struct sample *sni_smp = NULL;
-#endif
+	struct sample *name_smp = NULL;
 	struct sockaddr_storage *bind_addr = NULL;
 	int proxy_line_ret;
 	int64_t hash = 0;
@@ -1373,13 +1371,11 @@ int connect_server(struct stream *s)
 	if (err != SRV_STATUS_OK)
 		return SF_ERR_INTERNAL;
 
-#ifdef USE_OPENSSL
-	if (srv && srv->ssl_ctx.sni) {
-		sni_smp = sample_fetch_as_type(s->be, s->sess, s,
-		                               SMP_OPT_DIR_REQ | SMP_OPT_FINAL,
-		                               srv->ssl_ctx.sni, SMP_T_STR);
+	if (srv && srv->pool_conn_name_expr) {
+		name_smp = sample_fetch_as_type(s->be, s->sess, s,
+		                                SMP_OPT_DIR_REQ | SMP_OPT_FINAL,
+		                                srv->pool_conn_name_expr, SMP_T_STR);
 	}
-#endif
 
 	/* do not reuse if mode is not http */
 	if (!IS_HTX_STRM(s)) {
@@ -1403,17 +1399,12 @@ int connect_server(struct stream *s)
 	/* 1. target */
 	hash_params.target = s->target;
 
-#ifdef USE_OPENSSL
-	/* 2. sni
-	 * only test if the sample is not null as smp_make_safe (called before
-	 * ssl_sock_set_servername) can only fails if this is not the case
-	 */
-	if (sni_smp) {
-		hash_params.sni_prehash =
-		  conn_hash_prehash(sni_smp->data.u.str.area,
-		                    sni_smp->data.u.str.data);
+	/* 2. pool-conn-name */
+	if (name_smp) {
+		hash_params.name_prehash =
+		  conn_hash_prehash(name_smp->data.u.str.area,
+		                    name_smp->data.u.str.data);
 	}
-#endif /* USE_OPENSSL */
 
 	/* 3. destination address */
 	if (srv && srv_is_transparent(srv))
@@ -1787,7 +1778,13 @@ skip_reuse:
 		return err;
 
 #ifdef USE_OPENSSL
-	if (!(s->flags & SF_SRV_REUSED)) {
+	/* Set socket SNI unless connection is reused. */
+	if (srv && srv->ssl_ctx.sni && !(s->flags & SF_SRV_REUSED)) {
+		struct sample *sni_smp = NULL;
+
+		sni_smp = sample_fetch_as_type(s->be, s->sess, s,
+		                               SMP_OPT_DIR_REQ | SMP_OPT_FINAL,
+		                               srv->ssl_ctx.sni, SMP_T_STR);
 		if (smp_make_safe(sni_smp))
 			ssl_sock_set_servername(srv_conn, sni_smp->data.u.str.area);
 	}
diff --git a/src/connection.c b/src/connection.c
index 97af8f65e..d186c2f01 100644
--- a/src/connection.c
+++ b/src/connection.c
@@ -2621,7 +2621,7 @@ INITCALL1(STG_REGISTER, cfg_register_keywords, &cfg_kws);
 /* Generate the hash of a connection with params as input
  * Each non-null field of params is taken into account for the hash calcul.
  */
-uint64_t conn_hash_prehash(char *buf, size_t size)
+uint64_t conn_hash_prehash(const char *buf, size_t size)
 {
 	return XXH64(buf, size, 0);
 }
@@ -2699,10 +2699,10 @@ uint64_t conn_calculate_hash(const struct conn_hash_params *params)
 
 	conn_hash_update(&hash, &params->target, sizeof(params->target), &hash_flags, 0);
 
-	if (params->sni_prehash) {
+	if (params->name_prehash) {
 		conn_hash_update(&hash,
-		                 &params->sni_prehash, sizeof(params->sni_prehash),
-		                 &hash_flags, CONN_HASH_PARAMS_TYPE_SNI);
+		                 &params->name_prehash, sizeof(params->name_prehash),
+		                 &hash_flags, CONN_HASH_PARAMS_TYPE_NAME);
 	}
 
 	if (params->dst_addr) {
@@ -2770,7 +2770,7 @@ int conn_reverse(struct connection *conn)
 			/* data cannot wrap else prehash usage is incorrect */
 			BUG_ON(b_data(&conn->reverse.name) != b_contig_data(&conn->reverse.name, 0));
 
-			hash_params.sni_prehash =
+			hash_params.name_prehash =
 			  conn_hash_prehash(b_head(&conn->reverse.name),
 			                    b_data(&conn->reverse.name));
 		}